Finite Group Databasebeta

← #21444488

Subgroups — #21444488

Order 7808.

344 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 344 conjugacy classes of subgroups — too many to draw. Only its 93 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14519774C211yesmaximal, characteristic
2#16839815C211yesmaximal, characteristic, complemented
3#16839505C214yesmaximal, complemented
4C61×#423C211yesmaximal, characteristic, complemented
5C22×D244—21no—
6C22×D244—21no—
7C22×D244C412yes—
8#14519774—21no—
9#14519774—21no—
10#14519774C412yes—
11#14519774C2212yes—
12C4⋊#92418C2212yescomplemented
13C22⋊#92418—21no—
14C4×#92418—21no—
15C2×M16×C61—21no—
16C2×C42×C61C2211yescharacteristic
17C4⋊C8×C61—21no—
18C4⋊C8×C61C2212yescomplemented
19C23×D61—22no—
20C22×C4×C61C2×C411yescharacteristic
21C22×C4×C61D411yescharacteristic
22C22×C4×C61D411yescharacteristic
23C2×D244—22no—
24C2×D244—22no—
25C2×D244—22no—
26C2×D244—22no—
27C2×D244—22no—
28C2×D244—44no—
29C2×D244—42no—
30C2×D244—42no—
31C2×D244—44no—
32C2×D244C2×C414yes—
33M16×C61—42no—
34C2×C8×C61—22no—
35C42×C61C2×C411yescharacteristic
36C42×C61D411yescharacteristic
37C42×C61D411yescharacteristic
38C42×C61C2311yescharacteristic
39C2×#92418—22no—
40C23×C61C22⋊C411yescharacteristic
41C22×D61—24no—
42C22×D61—44no—
43C22×D61—44no—
44C22×D61—44no—
45C2×C4×C61—22no—
46C2×C4×C61—22no—
47C2×C4×C61C22⋊C411yescharacteristic
48C2×C4×C61C22⋊C411yescharacteristic
49C2×C4×C61C22⋊C411yescharacteristic
50C2×C4×C61D812yes—
51C2×C4×C61SD1612yes—
52C2×C4×C61C22×C411yescharacteristic
53C2×C4×C61C2×D411yescharacteristic
54C2×C4×C61C2×D411yescharacteristic
55D244—44no—
56D244—44no—
57D244—44no—
58D244—44no—
59D244—42no—
60D244—42no—
61D244—44no—
62C8×C61—42no—
63#92418—42no—
64C22×C61—21no—
65C22×C61—21no—
66C22×C61#10212yes—
67C22×C61C2×C22⋊C411yescharacteristic
68C2×D61—44no—
69C2×D61—44no—
70C2×D61—44no—
71C2×D61—88no—
72C4×C61—21no—
73C4×C61—21no—
74C4×C61#10012yes—
75C4×C61#10212yes—
76C4×C61C2×D811yescharacteristic
77C4×C61C2×SD1611yescharacteristic
78C4×C61AGL(1,ℤ/8)12yes—
79#1545—611nomaximal, Sylow
80C2×C61—22no—
81C2×C61C2×#10011yescharacteristic
82C2×C61C2×#10211yescharacteristic
83C2×C61#41811yescharacteristic
84D61—84no—
85C2×#127—611no—
86#431—611no—
87#423D6111yescharacteristic, complemented
88#331—614no—
89C61#154511yescharacteristic, complemented, Sylow
90C22×D4—612no—
91C22×D4—1221no—
92C22×D4—1221no—
93C2×M16—21no—
94#127—612no—
95#127—612no—
96#127—1221no—
97#127—1221no—
98C2×C42C2×D6111yescharacteristic
99C4⋊C8—21no—
100C4⋊C8—612no—
101C4⋊C8C2×D6112yescomplemented
102C22⋊C8—1221no—
103C4×C8—1221no—
104C24—1222no—
105C2×D4—614no—
106C2×D4—1222no—
107C2×D4—1222no—
108C2×D4—1222no—
109C2×D4—1222no—
110C2×D4—1222no—
111C2×D4—2444no—
112C2×D4—2444no—
113C2×D4—2442no—
114C2×D4—2442no—
115C22×C4C4×D6111yescharacteristic
116C22×C4D24411yescharacteristic
117C22×C4C22⋊D6111yescharacteristic
118M16—42no—
119C2×C8—22no—
120C2×C8—1222no—
121C42C4×D6111yescharacteristic
122C42D24411yescharacteristic
123C42C22⋊D6111yescharacteristic
124C42C22×D6111yescharacteristic
125C23—1224no—
126C23—2444no—
127C23—2444no—
128C23—2444no—
129C23#1175819811yescharacteristic
130D4—2444no—
131D4—2444no—
132D4—2444no—
133D4—2444no—
134D4—2442no—
135D4—2442no—
136D4—2444no—
137C2×C4—22no—
138C2×C4—22no—
139C2×C4#1175819811yescharacteristic
140C2×C4#1175819811yescharacteristic
141C2×C4#1175819811yescharacteristic
142C2×C4#1175819912yes—
143C2×C4#1175820112yes—
144C2×C4C2×C4×D6111yescharacteristic
145C2×C4C2×D24411yescharacteristic
146C2×C4C2×C22⋊D6111yescharacteristic
147C8—42no—
148C8—2442no—
149C22—21no—
150C22—21no—
151C22—4888no—
152C22—2444no—
153C22—2444no—
154C22—2444no—
155C22#1451969712yes—
156C22C2×#1175819811yescharacteristic
157C4—21no—
158C4—21no—
159C4#1451969312yes—
160C4#1451969712yes—
161C4C2×#1175819911yescharacteristic
162C4C2×#1175820111yescharacteristic
163C4#1451980512yes—
164C2—22no—
165C2—4884no—
166C2C2×#1451969311yescharacteristic
167C2C2×#1451969711yescharacteristic
168C2#1683976811yescharacteristic
subgroupG/H
centerC22C2×#11758198
commutatorC2×C4×C61C22×C4
FrattiniC42C22×D61
FittingC61×#423C2
socleC22×C61C2×C22⋊C4
hypercenter#423D61
hypocenterC61#1545
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #423

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. #16839815C2semidirect
3. #16839505C2semidirect
4. C61×#423C2semidirect
12. C4⋊#92418C22semidirect
18. C4⋊C8×C61C22semidirect
87. #423D61semidirect
89. C61#1545semidirect
101. C4⋊C8C2×D61semidirect